Order Equalities in Different Metrics for Moduli of Smoothness of Various Orders
Order Equalities in Different Metrics for Moduli of Smoothness of Various Orders is a scholarly work, published in 2018 in ''Ural mathematical journal''. The main subjects of the publication include pure mathematics, Quasi-Monte Carlo method, pi, mathematical analysis, smooth function, Ω/ω, stock order, modulus, monotonic function, Fourier series, mathematics, geometric function theory, and combinatorics. The authors obtain order equalities for the \(k\)th order \(L_{q}(T)\)-moduli of smoothness \(\omega_{k}(f;\delta)_{q}\) in terms of expressions that contain the \(l\)th order \(L_{p}(T)\)-moduli of smoothness \(\omega_{ l }(f;\delta)_{p}\) on the class of periodic functions \(f\in L_{p}(T)\) with monotonically decreasing Fourier coefficients, where \(1